How to Divide Fractions
In arithmetic, dividing fractions is much tricky but not difficult. If we ignore the reciprocal it is similar to the multiplication of fractions. In this section, we will learn how to divide fractions.
We can also divide a fraction by applying the division symbol (÷) between dividend and divisor. The fraction that is left of the division symbol is called the dividend, and the fraction that is right to the division symbol is called the divisor.
Methods of Dividing Fractions
There are two methods to divide fractions.
- Invert and Multiply Method
- Common Denominator Method
We can use both the methods in the following cases:
- when the denominators are the same
- when the denominators are different
Invert and Multiply Method
It is the easiest and commonly used method to divide fractions. In this method, first, we find the reciprocal (invert) of the divisor. After that multiply the dividend by the reciprocal. Do not use this for a complex problem.
- Find the reciprocal of the divisor fraction by swapping the numerator and denominator.
- Multiply the dividend fraction by the reciprocal.
- Simplify the fraction if required.
Suppose, 
and 
are two fractions and we want to divide by then:
Suppose, and are two fractions and we want to divide by then:
It is because if we find the reciprocal of the divisor, we get 
. Now multiply the dividend by the reciprocal, we get:
Solution:
In the above question, 
is the dividend and 
is the divisor.
Step 1: Find the reciprocal of the divisor.
Step 2: Multiplying dividend by the reciprocal.
Hence, on dividing by , we get 
as quotient.
Common Denominator Method
In this method, we make the denominators of both fractions the same. It is the most correct method to divide fractions. Find a common denominator and convert each fraction to its equivalent value.
- Now denominators are the same, we will divide the numerators only.
- Simplify the fraction if required.
Note: When converting the fraction to its equivalent value, multiply the same number in numerator and denominator.
Solution:
In the above question, 
is the dividend and 
is divisor.
Step 1: To find the common denominator, we will multiply by 5, and by 4.
Step 2: Divide the numerator of the fractions.
Hence, on dividing by , we get as quotient.
Solution:
In this question, 
is the dividend and 
is the divisor having the same denominator. So, we will divide the numerator only, i.e. 
.
Hence, on dividing by , we get as quotient.
Dividing Fraction and Whole Number
We can also divide a fraction by whole number or vice-versa. While dividing a fraction by the whole number, convert the whole number into a fraction by putting 1 in the denominator. It does not change the value. After that solve the question by using any one method that we have discussed above.
Solution:
In this question, the divisor is not in the fractional form. First, we will convert the whole number (7) into a fraction, i.e.,
. Now we have converted the question into the following:
Step 1: Find the reciprocal of the divisor.
Step 2: Multiplying dividend by the reciprocal.
Hence, on dividing 
by 7, we get 
as quotient.
Solution:
In this question, the dividend is not in the fractional form. First, we will convert the whole number (13) into a fraction, i.e.,
. Now we have converted the question into the following:
Step 1: Find the reciprocal of the divisor.
Step 2: Multiplying dividend by the reciprocal.
Hence, on dividing 13 by 
, we get 104 as quotient.
Dividing Mixed Fraction
When dealing with the mixed fraction, follow the steps given below:
- Convert the mixed fractions into an improper fractions.
- Find the reciprocal of the divisor fraction by swapping the numerator and denominator.
- Multiply the dividend fraction by the reciprocal.
- Simplify the fraction if required.
Solution:
Step 1: Convert the mixed fraction into an improper fraction, that is:
Step 2: Find the reciprocal of the divisor, that is:
Step 3: On multiplying the dividend fraction by reciprocal, we get:
Dividing More Than Two Fractions
We use the inverse and multiply method when any number of fractions is given for division. After this simplify the fraction, if required.
Solution:
Write the first fraction the same, and apply inverse, and multiply method in other fractions. Simplify the fraction, if required.
